The Life of Pi (π): From Archimedes to Eniac and Beyond

Jonathan M. Borwein, Frsc, Faa

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Preamble: Pi and Popular Culture
The desire to understand , the challenge, and originally the need, to calculate ever more accurate values of , the ratio of the circumference of a circle to its diameter (see Figure 1), has challenged mathematicians — great and less great — for many many centuries and, especially recently,  has provided compelling examples of computational mathematics. Pi, uniquely in mathematics is pervasive in popular culture and the popular
imagination.2
I shall intersperse this largely chronological account of Pi’s mathematical status with examples of its ubiquity. More details will be found in the selected references at the end of the chapter — especially in Pi: a Source Book [7]. In [7] nearly all material not otherwise referenced may be followed up upon, as may much other material, both serious and fanciful. More recent unsubstantiated assertions are covered in www.carma.newcastle.edu.au/~jb616/piday.pdf. Other interesting material is to be found in [18], which
includes attractive discussions of topics such as continued fractions and elliptic integrals.
Fascination with  is evidenced by the many recent popular books, television shows, and movies — even perfume — that have mentioned . In the 1967 Star Trek episode “Wolf in the Fold,” Kirk asks Aren’t there some mathematical problems that simply can’t be solved? And Spock ‘fries the brains’ of a rogue computer by telling it: Compute to the last digit the value of Pi. The May 6, 1993 episode of The Simpsons has the character
Apu boast I can recite pi to 40,000 places. The last digit is one.

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